Question

Find the distance between the points (9, 8) and (5, 3).

Write your answer as a whole number or a fully simplified radical expression. Do not round,

___ unit

Answer 1

`√(41)` units

Explanation:

To find the distance between two points, we can use the Pythagorean theorem by creating a right-angled triangle where sides a and b are the distances between the y-coordinates and x-coordinates of each point.

First let's find the distance between the x-coordinates:

(9,8): x-coordinate is 9, and (5,3): x-coordinate is 5.

9 - 5 = 4

The first side of our triangle is 4 units.

y-coordinates:

8 - 3 = 5

The second side of our triangle is 5 units.

`a^(2) +b^(2) =c^(2)`

`4^(2) +5^(2) =c^(2) \\16 +25 =c^(2) \\41 = c^(2) \\√(41) =\sqrt{c^(2) } \\√(41) = c`

Squareroot 41 is fully simplified as 41 is a prime number.

I have attached a picture to help visualize the triangle.

Hope this helped!